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Thread: Can anyone help me with this prob?

  1. #1
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    Can anyone help me with this prob?

    Let $\displaystyle U\subseteq R^n$ be an open set if $\displaystyle \forall x\in U $ there exists an r > 0 such that B(x,r) $\displaystyle \subseteq U$. B(x.r) meaning a ball centered on x with radius r.

    1) Let a $\displaystyle \in R^n$. Prove that for all $\displaystyle \epsilon > 0 $ B(a,$\displaystyle \epsilon$) is open

    2) Show that if $\displaystyle U_1, .... ,U_n$ are open in $\displaystyle R^n$ then $\displaystyle U_1\cap ..... \cap U_n$ also open
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  2. #2
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    Anyone?
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